# Math Help - rewrite complex number

1. ## rewrite complex number

who know how to convert z/(z^2+9) to z/(z+3i)/(z-3i)?i really do not have any idea how the book convert it.

2. Hello,

x²+9=x²-(9i)²

What else ?

3. no,look carefully at the question,i want to ask why z^2+9=(z+3i)/(z-3i)

4. This is not possible

Perhaps they meant $\frac{\frac{z}{z+3i}}{z-3i}$ which is $\frac{z}{(z+3i)(z-3i)}$

5. thanks,i think you are right.by the way,in another question,i saw it write 1/(z^2+1)=(1/2i)/(z-i) - (1/2i)/(z+i).how they did it?

6. Woah, it's better when you put the parenthesis where it has to go

$\frac{1}{z^2+1}=\frac{1}{(z-i)(z+i)}=\frac{a+bi}{z-i}+\frac{c+di}{z+i}$

$=\frac{(a+bi)(z+i)+(c+di)(z-i)}{z^2+1}$

The numerator has to be equal to 1.

So develop, then group the terms including z and write that its coefficient must be null since z doesn't appear in "1".
Solve for a, b, c and d